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Mathematical Problems in Engineering
Volume 2015, Article ID 960380, 12 pages
http://dx.doi.org/10.1155/2015/960380
Research Article

Study and Simulation on Discrete Dynamics of Bertrand Triopoly Team-Game

1Group of Nonlinear Dynamics and Chaos, College of Management and Economics, Tianjin University, Tianjin 300072, China
2College of Science, Tianjin University of Science and Technology, Tianjin 300457, China

Received 4 December 2014; Accepted 9 February 2015

Academic Editor: Domenico Mundo

Copyright © 2015 Lijian Sun and Junhai Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A Bertrand Triopoly team-game model is considered in which two firms with bounded rational expectations make up a cooperative team and allocate common profits proportionate to their marketing strength. The existence and three-dimensional stable regions of the fixed points are investigated. Complex effects of on bifurcation scenarios and profits are displayed by parameter basin plots and average profits charts. Impact of assigning weight on stable regions, 2D-bifurcation phase portraits, and the average profits is investigated. We find and can cause chaos; chaos resulting from adjustment speed is harmful to all the players as for profits, while chaos resulting from is conducive to firm 3. Basins of attraction are investigated and we find that the attraction domain will become smaller with increase of price modification speed.